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Zbl 1213.90233
Sun, Min
Merit functions and equivalent differentiable optimization problems for the extended general variational inequalities. (English)
[J] Int. J. Pure Appl. Math. 63, No. 1, 39-49 (2010). ISSN 1311-8080

Summary: We study some merit functions and equivalent differentiable optimization problems for the extended general variational inequalities involving three operators, which was introduced and studied by {\it M. A. Noor} [Projection iterative methods for extended general variational inequalities, J. Appl. Math. Comput. 32, No.~1, 83--95 (2009)] very recently. Using the projection technique, we obtain some error bounds for the solution of extended general variational inequalities under some mild conditions, and then formulate the extended general variational inequalities as differentiable constrained (or unconstrained) optimization problems. We also prove that the extended general variational inequalities have a unique solution under some conditions.

MSC 2000:: *90C30 Nonlinear programming
90C33 Complementarity problems

Keywords: error bounds

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Zentralblatt MATH Berlin [Germany]